Problem: Simplify the following expression: $a = \dfrac{-2q^2 + 10q - 8}{q - 1} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-2$ , so we can rewrite the expression: $ a =\dfrac{-2(q^2 - 5q + 4)}{q - 1} $ Then we factor the remaining polynomial: $q^2 {-5}q + {4} $ ${-1} {-4} = {-5}$ ${-1} \times {-4} = {4}$ $ (q {-1}) (q {-4}) $ This gives us a factored expression: $\dfrac{-2(q {-1}) (q {-4})}{q - 1}$ We can divide the numerator and denominator by $(q + 1)$ on condition that $q \neq 1$ Therefore $a = -2(q - 4); q \neq 1$